A deformable system is in equilibrium if the sum of the external virtual work and the internal virtual work is zero for virtual displacements ¿u which are kinematically admissible.

The major governing equations are summarized

IQ JQ JTt

39 Note that the principle is independent of material properties, and that the primary unknowns are the displacements.

■ Example 13-1: Tapered Cantiliver Beam, Virtual Displacement

Analyse the problem shown in Fig. 13.2, by the virtual displacement method. Solution:

1. For this flexural problem, we must apply the expression of the virtual internal strain energy as derived for beams in Eq. 13.25. And the solutions must be expressed in terms of the displacements which in turn must satisfy the essential boundary conditions.